Polygon Smoothing Nurbs Curves and Surfaces

Q. Li (UK)

Keywords

CAGD, NURBS, shape parameters, tension control, poly
gon smoothing.

Abstract

In conventional spline geometric shape design, each part of
a designed object always evolves the same number of con
trol points. This has been a disadvantage of the spline based
geometric shape design schemes as much more points than
necessary may be required to specify a shape. In this paper,
NURBS are generalized into Polygon Smoothing NURBS
(PS-NURBS) by introducing a new set of shape parameters
into conventional spline basis functions. The newly intro
duced parameters provide additional facilities for the free
form geometric object design. The most signiﬁcant fea
ture of this newly proposed spline scheme is that the num
ber of control points used for different parts of a geomet
ric shape can be varied according to design requirements.
With this technique, a geometric shape can be designed to
approximate the speciﬁed control polygon or control mesh
smoothly with any required precision. Compared with con
ventional NURBS, the proposed technique allows the de
signers to produce a much richer set of geometric shapes
with a relatively smaller set of control points.